Prime p₀= 2386965421141939871 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 58 2 16 2 130 2 16 2 58 2 (?)
a_n: 0 2 60 62 78 80 210 212 228 230 288 290
All 12 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 290
Found by: Landjunge
db: batch=81, k=12, 2 58 2 16 2 130

SPT(18)	2386963887532774699	0 4 48 114 130 142 144 168 198 244 274 298 300 312 328 394 438 442	-1533609165172
STPT(10)	2386964018348763611	0 2 6 8 18 20 30 32 36 38	-1402793176260
SPT(16)	2386964094514864819	0 22 28 30 40 58 180 190 210 220 342 360 370 372 378 400	-1326627075052
SPT(16)	2386965103225568639	0 30 78 132 140 182 212 218 222 228 258 300 308 362 410 440	-317916371232
SPT(16)	2386965204617110219	0 60 70 90 100 120 172 240 244 312 364 384 394 414 424 484	-216524829652
STPT(10)	2386965283293009239	0 2 18 20 30 32 42 44 60 62	-137848930632
STPT(10)	2386966320936410999	0 2 42 44 60 62 78 80 120 122	899794471128
SPT(16)	2386966439680775377	0 22 36 40 54 90 102 154 222 274 286 322 336 340 354 376	1018538835506
STPT(10)	2386966503018619187	0 2 30 32 42 44 54 56 84 86	1081876679316
SPT(16)	2386966506163602191	0 2 72 80 90 98 138 152 168 182 222 230 240 248 318 320	1085021662320
SPT(16)	2386966724455352629	0 18 28 30 72 84 148 154 228 234 298 310 352 354 364 382	1303313412758